modeling and analysis for surface roughness and material

MultiCraft

International Journal of Engineering, Science and Technology

Vol. 3, No. 8, 2011, pp. 248-270

INTERNATIONAL JOURNAL OF

ENGINEERING, SCIENCE AND TECHNOLOGY

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Modeling and analysis for surface roughness and material removal rate in machining of UD-GFRP using PCD tool

Surinder Kumar1*; Meenu Gupta2; P.S. Satsangi3 and H.K. Sardana4

1Department of Mechanical Engineering, National Institute of Technology, Kurukshetra 136119, INDIA 2Department of Mechanical Engineering, National Institute of Technology, Kurukshetra 136119, INDIA

3Department of Mechanical Engineering, PEC University of Technology, Chandigarh 160012, INDIA 4Department of Computational Instrumentation, CSIO, Chandigarh 160030, INDIA

*Corresponding Author: e-mail: [email protected]; Phone: 09466267889

Abstract In the present paper, an effective approach for the optimization of turning parameters based on the Taugchi’s method with regression analysis is presented. This paper discusses the use of Taugchi’s technique for minimizing the surface roughness and maximizing the material removal rate in machining unidirectional glass fiber reinforced plastics (UD-GFRP) composite with a polycrystalline diamond (PCD) tool. A multiple objective utility model has been studied to optimize both the dependent parameters. Experiments were conducted based on the established Taguchi’s technique L18 orthogonal array on a lathe machine. The cutting parameters considered were tool nose radius, tool rake angle, feed rate, cutting speed, depth of cut and cutting environment (dry, wet and cooled) on the surface roughness and material removal rate produced. The performances of the cutting tool were evaluated by measuring surface roughness and material removal rate. A second order mathematical model in terms of cutting parameters is also developed using regression modeling. The results indicate that the developed model is suitable for prediction of surface roughness and material removal rate in machining of unidirectional glass fiber reinforced plastics (UD-GFRP) composites. The predicted values and measured values are fairly close to each other. The results are confirmed by further experiments. Keywords: UD-GFRP composites, ANOVA, multi response optimization, utility concept, regression modeling, surface roughness, material removal rate, polycrystalline diamond (PCD) tool. DOI: http://dx.doi.org/10.4314/ijest.v3i8.20

1. Introduction Fiberglass composites are replacing many of the materials used in industries as they are economical. Glass fibre reinforced polymers (GFRP) are being used in variety of applications that include oil, gas and corrosive environments. Machining of glass fiber-reinforced polymer (GFRP) composite materials have always been a challenge due to host of difficulties encountered such as fiber pull-out, fiber fuzzing, matrix burning, and fiber-matrix debonding leading to subsurface damage, reduced strength and short product service life. The necessities of machining FRP composites come from the requirement of the conversion of raw composite material into engineering component despite the ability to fabricate near-net shape components. The FRPs are one of the ‘difficult-to-machine’ materials because of the fibre arrangement. Machining of composite parts creates discontinuity in the fibre and thus affects the performance of the part. Besides, the mechanism of material removal is different from that of single-phased materials, such as metals. The material removal process is quite complex. Many variables such as the workpiece material, the cutting tool material, the rigidity of the machine, the set up, the cutting feed, speed, tool wear and chip control must be considered. Arola and Ramulu (1997) as well as Mahdi and Zhang (2001) applied the finite element method to investigate the cutting of FRPs but the former adopted a homogenized material model and the latter considered the micro details of individual fibre-tool interactions. Fiber reinforced materials generally contain two or more constituents. They are matrix and the fiber to name, to take advantage of the best properties of those, without compromising on the weakness of either. Generally the matrix is of ductile and

Kumar et al. / International Journal of Engineering, Science and Technology, Vol. 3, No. 8, 2011, pp. 248-270

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fiber is of brittle in nature. In fiber reinforced composite materials, fibers act as a load carrying medium and the matrix acts as a load transporting medium (Mohan et al., 2005). Machining glass fibre composite is still a major problem, because of their inert nature, high hardness, and refractoriness (Jain et al., 2002). Because of their different applications, the need for machining FRP material has not been fully eliminated. Glass fibre reinforced plastics (GFRPs) are extremely abrasive, thus proper selection of the cutting tool and cutting parameters is very important for a perfect machining process (Davim et al., 2009). The surface integrity of a GFRP machined composite is hard to control due to varying mechanical properties of the fibre and the matrix (Zang, 2009). Caprino et al. (1998) carried out orthogonal cutting tests using high speed steel tools, to determine the trend of the principal forces on unidirectional-GFRP. The cutting direction was held parallel to the fibre orientation while the tool rake, relief angle and the depth of the cut were varied. The authors concluded that the frictional force generated by the chip sliding up the tool face was negligible so that the tool face-chip interaction resulted in a force practically normal to the face itself. The forces arising at the top flank and cutting edge were a considerable part of the overall cutting forces. The vertical force, due to the compression of the tool against the freshly generated work material surface, was dependant on all the machining parameters. Vertical force decreased with both the rake and relief angles and linearly increased by increasing the depth of the cut. Wang and Zhang (1999) investigated the cutting of carbon fibre-reinforced composites and found that the machinability and surface integrity are mainly controlled by fibre-orientation. The role of these parameters is to evaluate the surface produced by a machining process and to quantify the amount of machining damage for different process parameters such as cutting speed, feed rate and depth of cut. It has been shown that lower the value of surface roughness, the better is the quality of machined surface. Roughness values also indicate changes in the mechanical properties of machined FRP. Studies have shown that with increasing roughness the fatigue strength and impact strength decreases (Ramulu and Arola, 1995). There is a significant difference between the machining of conventional metals and their alloys and that of FRP materials (Ramulu et al, 1991). This is because FRP materials are anisotropic, inhomogeneous and are mostly prepared in laminate form before undergoing the machining process. Unlike the case of homogeneous metals, where the machining is associated with plastic deformation and shearing, the machining of FRP composites is associated with plowing, cutting and cracking (Wang et al., 1995 and Pwu et al., 1998), it is necessary to control/minimize the occurrence of such defects which poses considerable machinability problems. (Hussain et al., 2010) developed a surface roughness prediction model for the machining of GFRP pipes using response surface methodology by using carbide tool (K20). Four parameters such as cutting speed, feed rate, depth of cut and work piece (fiber orientation) were selected to minimize the surface roughness. It was found that, the depth of cut shows a minimum effect on surface roughness as compared to other parameters. (Ramesh et al., 2008) developed a surface roughness prediction model for the machining of CVD (TiN–TiCN–Al2O3–TiN) using response surface methodology by using coated carbide insert under different cutting conditions using taguchi's orthogonal array. Three parameters such as cutting speed, feed rate and depth of cut were selected to minimize the surface roughness. It was found that, the feed rate is the factor, which has great influence on surface roughness, followed as compared to other parameters. Several methodologies were developed to solve the multi-response optimization problems. Byrne and Taguchi (1987) presented a case where the responses were optimized independently using Taguchi’s approach and then the results were compared subjectively to select the best levels in terms of the responses of interest. (Logothetis and Haigh, 1988) employed multiple regressions and a linear programming approach for multi response optimization by Taguchi method. This procedure was computationally complex thereby making its use difficult on shop floor. (Shiau, 1990) solved the multi-response problem by assigning the weights to S/N ratio of each quality characteristic and then summing up the weighted S/N ratios for the measurement of overall performance of a process. (Singh et al., 2002) used multi-response optimization through utility concept and Taguchi method for optimization of the quality characteristics of MAFM process. Isik et al. (2009) proposed an approach for turning of a glass fiber reinforced plastic composites using cemented carbide tool. Three parameters such as depth of cut, cutting speed and feed rate were selected to minimize the Tangential and feed force. Weighting techniques was used. The idea of this technique consists in adding all the objective functions together using different coefficients for each. It means that multicriteria optimization problem is changed to a scalar optimization problem by creating one function of the form. It was found that this technique will be more economical to predict the effect of different influential combination of parameters. Rajasekaran et al. (2011) used fuzzy logic for modeling and prediction of CFRP work piece. Three parameters such as depth of cut, feed rate and cutting speed were selected to minimize the surface roughness. Cubic boron nitride tool was used for turning process. It was found that the fuzzy logic modeling technique can be effectively used for the prediction of surface roughness in machining of CFRP composites. GFRP is a cheaper option than Carbon or Kevlar, so GFRP rods were used in this work. In this study, the surface roughness and MRR were measured on machining UD-GFRP composite materials. Hussain et al. (2011) developed a surface roughness and cutting force prediction model for the machining of GFRP tubes using response surface methodology by using carbide tool (K20), cubic boron nitride (CBN) and polycrystalline diamond (PCD). Four parameters such as cutting speed, feed rate, depth of cut and work piece (fiber orientation) were selected to minimize the surface roughness and cutting forces. It was found that, the polycrystalline diamond (PCD) cutting tool is better. As seen from the literature, only limited work has been carried out on the machinability aspects of unidirectional glass fiber reinforced plastic (UD-GFRP) composite. Thus, this present work aims at investigating the effects of tool nose radius, tool rake angle, feed rate, cutting speed, cutting environment (dry, wet and cooled) and depth of cut on some aspects of machinability of UD-GFRP composites. In the present investigation, the machinability aspects have been evaluated in terms of surface roughness and material removal rate during the


250

turning of UD-GFRP composites using PCD tools. Regression analyses are applied to identify the best levels of cutting parameters and their significance. Insignificant parameters are not taken into consideration in this Regression modelling. To convert the different performance into a single performance unit, linear regression modeling is used. Also these techniques are effectively used for optimization of parameters and for modeling as well. 2. Experimental Procedure 2.1 Material In the present study, pultrusion processed unidirectional glass fiber reinforced plastic composite rods is used. The diameter of the rod taken is 42 mm and length 840 mm. The fiber used in the rod is E-glass and resin used is epoxy and properties of material used are shown in Table 1. Table 1 Mechanical and Thermal Properties of the UD-GFRP Material 2.2 Method The Taguchi method is a commonly adopted approach for optimizing design parameters. The method was originally proposed as a means of improving the quality of products through the application of statistical and engineering concepts. It is a method based on Orthogonal Array (OA) experiments, which provides much-reduced variance for the experiment resulting is optimum setting of process control parameters. Orthogonal Array (OA) provides a set of well-balanced experiments (with less number of experimental runs) and Taguchi’s signal-to-noise ratios (S/N), which are logarithmic functions of desired output, serves as objective function in the optimization process. This technique helps in data analysis and prediction of optimum results. In order to evaluate optimal parameter settings, Taguchi method uses a statistical measure of performance called signal-to-noise ratio. The S/N ratio takes both the mean and the variability into account. The S/N ratio is the ratio of the mean (Signal) to the standard deviation (Noise). The ratio depends on the quality characteristics of the product/process to be optimized. The standard S/N ratios generally used are as follows:- Nominal-is-Best (NB), lower-the-better (LB) and Higher-the-Better (HB). The optimal setting is the parameter combination, which has the highest S/N ratio. In this study, material removal rate is taken “higher the better” type and surface roughness is taken “lower the better”. The corresponding loss function can be expressed as follows (Ross, 1988). Smaller the better:

S/N = 10 Log ∑ 21 yn

(1)

Larger the better:

S/N = 10 Log ∑ 211yn

(2)

Sr. No. Particular Value Unit 1 2 3 4 5 6 7 8 9

10 11 12 13 14 15

Glass Content (by weight) Epoxy Resin content (by weight) Reinforcement, unidirectional Water absorption Density Tensile Strength Compression Strength Shear Strength Modulus of elasticity Thermal Conductivity Weight of Rod 840 mm in length Electrical strength (Radial): Working Temperature Class: Martens Heat Distortion Temperature Test in oil : (1) At 20° C: (2) At 100° C:

75±5 25±5 ‘E’ Glass Roving 0.07 1.95-2.1 6500 or (650) 6000 or (600) 255 3200 or (320) 0.30 2.300 3.5 Class ‘F’ (155 ) 210 20 KV/cm 20 KV/cm (50 KV / 25 mm)

% % --- % gm/cc Kg / cm2 or (N/mm2) Kg / cm2 or (N/mm2) Kg / cm2 or (N/mm2) Kg / cm2 or (N/mm2) Kcal /Mhc° Kgs KV / mm Centigrade Centigrade KV/cm


251

“Where n is the number of observations, y is the observed data”. 2.3 Present Problem Taguchi design of experiment is a powerful analysis tool for modeling and analyzing the influence of control factors on performance output. The initial step in the Taguchi model is to build up an input-output database required for the optimization through the turning experiments. In order to have a complete knowledge of turning process over the range of parameters selected, a proper planning of experimentation is essential to reduce the cost and time. In order to identify the process parameters that may affect the machining characteristics of centre lathe machined parts an Ishikawa cause effect diagram was constructed and is shown in Figure 1. The Ishikawa cause-effect gives analysis from the observation based on previous research. The identified process parameters are:

Cutting Tool Cutting Parameters Cutting Speed Tool Material

Type of Coating Feed Rate Flow & Tool Geometry Type of Coolant Depth of Cut

Dry Cooled

Diameter Wet Cutting Environment Workpiece Parameters Cutting Parameters: cutting speed, feed rate, depth of cut, flow of current and environment Cutting tool related Parameters: tool material, tool geometry, type of coating and inserts condition. Work piece based Parameters: type of material, mechanical properties and diameter. Cutting Environment: dry, wet and cooled environment

Figure 1: Ishikawa Cause-Effect Diagram of a Turning Process

Although Taguchi's approach towards robust parameter design introduced innovative techniques to improve quality, a few concerns regarding his philosophy have been raised. Some of these concerns relate to the signal to noise ratios defined to reduce variations in the response and some others are related to the absence of the means to test for higher-order control factor interactions when his orthogonal arrays are used as inner arrays for the design. For these reasons, other approaches to carry out robust parameter design have been suggested including response modeling and the use of lnsi

2 in the place of the signal to noise ratios in the dispersion model. In response modeling, the noise factors are included in the model as additional factors, along with the other control factors. The most significant limitation of these techniques relates to process data availability and quality. Current databases were not designed for process improvement, resulting in potential difficulties for the Taguchi experimentation, where available data does not explain all the variability in process outcomes. The limitation of OA is that it can only be applied at the initial stage of the product/process design system. There are some situations whereby OA techniques are not applicable, such as a process involving influencing factors that vary in time and cannot be quantified exactly (Weibull, 2012).

Mechanical Properties

Quality of Turned Parts

Type of Material


252

The Taguchi’s mixed level design was selected as it was decided to keep two levels of tool nose radius. The rest five parameters were studied at three levels. Two level parameter has 1 DOF, and the remaining five three level parameters have 10 DOF, i.e., the total DOF required will be 11 [= (1*1+ (5*2)]. The most appropriate orthogonal array in this case is L18 (21 * 37) OA with 17 [= 18-1] DOF. Standard L18 OA with the parameters assigned by using linear graphs is used. The unassigned columns will be treated as error. According to the Taguchi design concept, a L18 orthogonal array is chosen for the experiments as shown in Table 2.

Table 2 Experimental Layout using L18 Orthogonal Array Expt. No. A B C D E F --- ---

1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18

1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2

1 1 1 2 2 2 3 3 3 1 1 1 2 2 2 3 3 3

1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3

1 2 3 1 2 3 2 3 1 3 1 2 2 3 1 3 1 2

1 2 3 2 3 1 1 2 3 3 1 2 3 1 2 2 3 1

1 2 3 2 3 1 3 1 2 2 3 1 1 2 3 3 1 2

1 2 3 3 1 2 2 3 1 2 3 1 3 1 2 1 2 3

1 2 3 3 1 2 3 1 2 1 2 3 2 3 1 2 3 1

The L18 orthogonal array has 18 rows corresponding to the number of tests. The parameters tool nose radius, tool rake angle, feed rate, cutting speed, cutting environment and depth of cut are assigned to columns (A, B, C, D, E, F) respectively as shown in Table 2. Out of which cutting environment parameters (dry, wet and cooled) are especially applied to composite rods. The cutting environment (dry, wet and cooled) on the workpiece was set during the machining of the rod, so as to obtain a comparative assessment of the performance of cutting environment which has not been studied earlier. So, it can be used for the cutting environment. The cutting fluid used in flooded machining is CASTROL water miscible soluble coolant contains 1:6 volumetric concentration is flushed at cutting zone. The spray is concentrated on rake and flank surface along the cutting edges, minimize the friction, lubricity abilities and reduce the tool wear (Kodandaram et al., 2010). Cutting environment: Wet (33-38° temperature) and Cooled (5-7° temperature) is used. The output responses used to measure the machinability are surface roughness and material

removal rate. The parameters selected, the designated symbols, and their ranges are given in Table 3.

Table 3 Control Parameters and their Level The machining tests were conducted on a conventional lathe machine as shown in Figure 2 with the following specifications: a height of center 220 mm, swing over bed 500 mm, spindle speed range 60 – 3000 rpm, feed range 0.04 – 2.24 mm /rev and main motor 11 kW. A tool holder SVJCR steel EN47 was used during the turning operation. The different cutting tool inserts as shown in Figure 3(a) & 3(b) are made of polycrystalline diamond. The geometry of the cutting tool VNMG insert 110404/110408 is as follow: NQA BS EN ISO 9001-2000, tool rake angle -6° (negative), 0°, and +6° (positive) and tool nose radius 0.4mm & 0.8mm. From these 54 data points, the suitable L18 array data points were chosen. With the finished product, the surface roughness values were measured. The surface roughness was measured by using Tokyo Seimitsu Surfcom 130A type instrument as shown in Figure 4. For each trial, experiments were replicated (three times). A statistical analysis of variance (ANOVA) is performed to see which process parameter is statistically significant for surface roughness and material removal rate property. The optimum condition for

Process Parameters

Design

Process Parameters Levels Level (1) Level (2) Level (3)

A B C D E F

Tool nose Radius / mm Tool Rake angle / Degree Feed rate / (mm/rev.) Cutting speed / (m/min.) & rpm Cutting environment Depth of cut / mm

0.4 (-6) 0.05

(55.42) 420 Dry (1)

0.2

0.8 (0) 0.1

(110.84) 840 Wet (2)

0.8

NIL (+6) 0.2

(159.66) 1210 Cooled (3)

1.4


253

surface roughness and material removal rate characteristic has been established through S/N data analysis aided by raw data analysis. Surface roughness and material removal rate data are analyzed to determine the effect of the various design parameters. The experimental results are then transformed into signal-to-noise (S/N) ratio. Taguchi recommends the use of S/N ratio to measure the quality characteristics deviating from the desired values. The material removal rate, in mm3/ sec., has been calculated from the following relation: Material Removal rate = It is the volume of material being removed per unit time the work piece,

Tc

LdLDMRR

22

44ππ

−= (3)

Where, D = initial dia in mm, d = final dia in mm, L = length in mm, f = feed rate in mm/rev. where Tc per pass is defined as: Tc = L /f N is the machining time, F =feed rate in mm/rev. L = length of the workpiece to be turned, N = spindle speed in rpm

Figure 2: Experimental set up

Figure 3(a): PCD cutting tool inserts used on the experiment

Figure 3(b): PCD cutting tool inserts used on the experiments


254

Figure 4: Surface Roughness Tester: - Tokyo Seimitsu Surfcom 130A

3. Results and Discussions The analysis is made using the popular software MINITAB 15 specifically used for design of experiment applications, Table 4 test data summary shows the experimental results for surface roughness, MRR and their S/N ratios based on the experimental parameter combinations.

Table 4 Test Data Summary for Surface Roughness and Material Removal Rate

Average

TRa = 1.812

–4.999

TMRR = 136.875

39.463 The mean response refers to the average value of the performance characteristic for each parameter at different levels. The average values of surface roughness for each parameter at levels 1, 2 and 3 are calculated. The main effects (raw data and S/N ratio) of the various process parameters when they change from the lower to higher levels can be visualized from the Figure 5 (a, b, c, d, e, f) shows the response graphs of surface roughness for this tool nose radius, tool rake angle, feed rate, cutting speed, cutting environment and depth of cut. It is clear from the Figure 5 (a, b, c, d, e, f) that the surface roughness is lowest at A2, B2, C2, D2, E1 and F2. Figure 5 (a-f) shows the effect of tool nose radius, tool rake angle, feed rate, cutting speed, cutting environment (dry, wet and cooled) and depth of cut on surface roughness in turning of UD-GFRP composites. The results indicated that the increase of tool nose radius reduce the surface roughness up to 0.8 mm as shown in Figure 5 (a). The surface roughness increased with increase in tool rake angle as shown in Figure 5 (b). The figure indicates that the surface roughness increased at higher feed rates and cutting speed as shown in Figure 5 (c & d). The reason being, the increase in the feed rate increases the heat generation and hence, tool wear, which resulted in the higher surface roughness. The increase in the feed rate also increases the chatter and it produces incomplete machining at faster traverse, which leads to higher surface roughness. At higher cutting speed debonding and fiber breakage are the reasons for poor surface roughness. The results indicated that the surface roughness increases with increase in cutting environment and depth of cut and is presented in Figure 5 (e & f).

Expt. No.

Ra Average Ra (µm)

S/N ratio (dB) MRR Average MRR (mm3/sec.)

S/N ratio (dB)

1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17

18

1.38/1.46/1.35 1.67/1.36/1.33 3.00/2.79/3.44 1.31/1.47/1.32 1.70/1.24/1.65 2.05/2.93/2.22 1.61/1.33/1.60 1.67/1.79/1.45 2.43/2.20/2.16 1.38/1.83/1.43 1.52/1.43/1.87 2.24/1.90/1.76 1.57/1.57/1.65 1.40/1.86/1.63 2.14/1.80/2.77

2.12/1.940/1.90 1.23/1.486/1.70 1.98/1.973/2.28

1.397 1.453 3.076 1.366

1.530 2.400

1.513 1.636 2.263 1.547 1.606 1.966 1.597

1.630 2.237 1.940 1.486 1.973

-2.90665 -3.29561 -9.79513 -2.72569 -3.77191 -7.71240 -3.63048 -4.31122 -7.10695 -3.86095 -4.17870 -5.91999 -4.06671 -4.30102 -7.13000 -5.77660 -3.51783 -5.97490

8.6/8.5/8.7 145.00/145.02/144.95 327.58/347.03/347.23 36.24/36.24/36.24 249.90/249.96/249.88 106.02/105.86/105.90 125.00/124.98/124.98 52.96/52.99/52.97 144.97/144.97/145.02 104.42/104.38/104.40 125.00/125.00/125.00 73.57/73.58/73.55 18.39/18.39/18.39 208.72/208.92/208.92 250.09/250.09/250.05 180.00/180.04/180.00 18.38/18.38/18.38 275.93/275.87/275.75

8.60 144.99 340.61

36.24 249.91 105.93 124.99 52.97 144.99 104.40 125.00 73.57 18.39 208.85 250.08 180.01 18.38 275.85

18.6888 43.2268 50.6354 31.1838 47.9558 40.5001 41.9373 34.4811 43.2266 40.3740 41.9382 37.3336 25.2916 46.3968 47.9615 45.1061 25.2869 48.8135


255

(a) (b)

(c) (d)

(e) (f) Figure 5 Response and S/N ratio (a) effect of tool nose radius, (b) effect of tool rake angle, (c) effect of feed rate, (d) effect of cutting speed, (e) effect of cutting environment and (f) effect of depth of cut The pooled version of ANOVA of the raw data and S/N ratio for surface roughness is given in Table 5(A) and 5(B). From Table 5(A) and 5(B), it is clear that parameters C, D and F significantly affect both, the mean and variation, in the surface roughness value. The average of three measurements has been taken as the value of the Ra for the purpose of the analysis. The optimum value of surface roughness is predicted at the selected levels of significant parameters. The percent contributions of parameters as quantified under column P of Table 5(A) and 5(B) reveal that the influence of feed rate in affecting surface roughness is significantly larger than the cutting speed and depth of cut. The percent contributions of feed rate (54.399 %), cutting speed (10.119%) and depth of cut (5.355%) in affecting the variation of surface roughness are significantly larger (95 % confidence level) as compared to the contribution of the other parameters as shown by Table 5(A).


256

Table 5(A) Pooled ANOVA (Raw Data: Surface Roughness)

SS = sum of squares, DOF = degrees of freedom, variance (V) = (SS/DOF), T = total, SS/ = pure sum of squares, P = percent contribution, e = error, Fratio = (V/error), Tabulated F-ratio at 95% confidence level * Significant at 95% confidence level.

Table 5 (B) S/N Pooled ANOVA (Raw Data: Surface Roughness)

The average values of material removal rate for each parameter at levels 1, 2 and 3 are calculated. The main effects (raw data and S/N ratio) of the various process parameters when they change from the lower to higher levels can be visualized from the Figure 6 (a, b, c, d, e, f). Figure 6 (a-f) shows that the response graph for material removal rate for parameters is highest at the (A2, B2, C3, D3, E3 and F3). The S/N ratio analysis also (Figure 6) suggests same levels of the parameters (A2, B2, C3, D3, E3 and F3) as the best levels for highest material removal rate of the unidirectional glass fiber reinforced plastic composite. The basic purposes of cutting fluid application are: (1) Cooling of the job and the tool to reduce the detrimental effects of cutting temperature on the job and the tool and (2) lubrication at the chip–tool interface and friction and thus the amount of heat generation. Figure 6 (a-f) shows the graph of material removal rate. The results indicated that the material removal rate increases with increase in tool nose radius, feed rate, cutting speed, cutting environment, depth of cut and moderate with increase in tool rake angle. The pooled version of ANOVA of the raw data and S/N ratio for material removal rate is given in Table 6(A) and 6(B). From Table 6(A) and 6(B), it is clear that parameters C, D and F significantly affect both, the mean and variation, in the material removal rate value. The percent contributions of parameters as quantified under column P of Table 6(A) and 6(B) reveal that the influence of depth of cut in affecting material removal rate is significantly larger than the feed rate and cutting speed. The percent contributions of depth of cut (52.168%), feed rate (26.179%) and cutting speed (8.838%) in affecting the variation of material removal rate are significantly larger (95 % confidence level) as compared to the contribution of the other parameters as shown by Table 6(A).

(a) (b)

Figure 6. Response and S/N ratio (a) effect of tool nose radius, (b) effect of tool rake angle

Source SS DOF V F ratio Prob. SS/ P (%) Tool nose radius(A) Tool rake angle(B) Feed rate(C) Cutting speed(D) Cutting Environment(E) Depth of cut(F) T

e (pooled)

0.07114 0.02324 6.94648 1.40654 0.29613 0.81130

1 2 2 2 2 2

0.07114 0.01162 3.47324 0.70327 0.14807 0.40565

0.07039

Pooled Pooled 49.34* 9.99*

Pooled 5.76*

0.321 0.848 0.000 0.000 0.135 0.006

--- ---

6.806 1.266

--- 0.670

--- ---

54.399 10.119

--- 5.355

12.51133 2.95649

53 42

12.51133 3.731

100.00 29.821

Source SS DOF V F ratio Prob. SS/ P (%) Tool nose radius(A) Tool rake angle(B) Feed rate(C) Cutting speed(D) Cutting Environment(E) Depth of cut(F)

T e (pooled)

0.0156 0.0314

46.5614 8.3717 1.1464 4.7120

1 2 2 2 2 2

0.0156 0.0157

23.2807 4.1858 0.5732 2.3560

0.4557

Pooled Pooled 51.09* 9.19*

Pooled 5.17*

0.859 0.966 0.000 0.015 0.350 0.050

--- ---

45.65 7.460

--- 3.801

--- ---

71.808 11.735

--- 5.979

63.5727 2.7343

17 6

63.5727 7.747

100.00 12.19


257

(c) (d)

(e) (f)

Figure 6. Response and S/N ratio (c) effect of feed rate, (d) effect of cutting speed, (e) effect of cutting environment and (f) effect of depth of cut.

Table 6(A) Pooled ANOVA (Raw Data: Material Removal Rate)

SS = sum of squares, DOF = degrees of freedom, variance (V) = (SS/DOF), T = total, SS/ = pure sum of squares, P = percent contribution, e = error, Fratio = (V/error), Tabulated F-ratio at 95% confidence level, * Significant at 95% confidence level.

Table 6(B) S/N Pooled ANOVA (Raw Data: Material Removal Rate

4. Regression Analysis Multiple linear regression equations were modeled for a relationship between process parameters in a bid to evaluate surface roughness and material removal rate for any combinations of factors levels in a range specified. The functional relationship between dependent output parameter with the independent variables under investigation could be postulated by Equation 4.


T e (pooled)

342 1739 129356 45233 5404 253033

1 2 2 2 2 2

342 869 64678 22616 2702 126516 1189

Pooled Pooled 54.41* 19.03* Pooled 106.43*

0.595 0.487 0.000 0.000 0.116 0.000

--- --- 126978 42855 --- 253032

--- --- 26.179 8.835 --- 52.168

485034 49927

53 42

485034 63006

100.00 12.99


T e (pooled)

2.47 5.27 363.35 216.91 4.10 803.17

1 2 2 2 2 2

2.47 2.63 181.68 108.46 2.05 401.58 2.50

Pooled Pooled 72.69* 43.40* Pooled 160.68*

0.359 0.405 0.000 0.000 0.484 0.000

--- --- 358.35 211.91 --- 798.17

--- --- 25.410 15.026 --- 56.597

1410.27 15.00

17 6

1410.27 42.5

100.00 3.01


258

Y = K (X1) a (X2) b (X3) c (4)

Where Y is dependent output variable such as surface roughness and material removal rate X�, X� and X�, are independent variables such as feed rate, cutting speed and depth of cut. The constants a, b and c are the exponents of independent variables. To convert the above non linear equation into linear form, a logarithmic transformation is applied into the above equation and written as Equation 5.

Log Y = log K + a. log(X1) + b. log(X2) + c.log (X3) (5)

This is one of the most popularly used data transformation methods for empirical model building. Now the above equation is written as Equation 6.

η = β0 + β1.x1 + β2.x2 + β3.x3 (6) Where, η is the true value of dependent surface roughness and material removal rate on a logarithmic scale, x1, x2 and x3 are respectively, the logarithmic transformation of the different parameters, while β0, β1, β2 and β3 are the corresponding parameters to be estimated. Due to the experimental error, the true response η = y-ε, where y is the logarithmic transformation of the measured surface roughness and material removal rate parameters and the ε is the experimental error. For simplicity the equation is rewritten as Ŷ = b0 + b1x1 + b2x2 + b3x3 (7) Where Ŷ is the predicted surface roughness and material removal rate value after logarithmic transformation and b0, b1, b2 and b3 are the estimates of the parameters, β1, β2 and β3, respectively. The values of b0, b1, b2 and b3 are found out by linear regression analysis, (second order model) which is conducted with MINITAB standard version software (MINITAB 15.0 for windows), using the experimental data. The first order model for surface roughness and material removal rate reveals lack of fitness due to high prediction errors for surface roughness and material removal rate. As a result, the below mentioned second order model has been developed and its form is given below.

Ŷ = b0 + b1x1 + b2x2 + b3x3 + b12x1x2 + b13x1x3 + b23x2x3 + b11x12 + b22x2

2 + b33x32 (8)

Insignificant parameters are not taken into consideration as shown in Table 7. The developed empirical model by regression analysis for surface roughness (Ra) and material removal rate (MRR) is given below: Ra = 5.87 + 2.43 x1 + (- 4.65) x2 + 0.009 x3 + (- 0.129) x1x2 + 0.065 x1x3+ 0.152 x2x3 + 0.944 x1

2 + 1.20 x22 + 0.339 x3

2

MRR= 0.005 + 1.52 x1 + 2.65 x2+ 1.08 x3 + (- 0.684) x1x2 + (- 0.347) x1x3 + (- 0.334) x2x3 + (- 0.325) x12 + (- 0.651) x2

2 + (- 0.250) x3

2

Predicted output values for surface roughness and material removal rate are calculated with the help of above equation and the given coefficients as shown in Table 7. It has been seen that relative error of surface roughness and material removal rate are well within limits.

Table 7 Empirical Expressions Developed by Second Order Model

Predictor Coefficient of surface roughness

Predictor Coefficient of material removal rate

bo X1 X2 X3 X1 X2 X1 X3 X2 X3 X1

2 X2

2 X3

2

5.87 2.43 - 4.65 0.009 - 0.129 0.065 0.152 0.944 1.20 0.339

bo X1 X2 X3 X1 X2 X1 X3 X2 X3 X1

2 X2

2 X3

2

0.005 1.52 2.65 1.08 - 0.684 - 0.347 - 0.334 - 0.325 - 0.651 - 0.250


259

Thus, it can be stated that empirical equation build by using second-order model can be used. Relative error between predicted and measured observed values for surface roughness and material removal rate is calculated and presented in Table 8. The significance of predictors, shown in Table 7, is also analyzed further as shown in Table 8

Table 8 Comparison between Experimental and Predicted Values of Surface Roughness and Material Removal Rate 5. Goodness of Fit for Surface Roughness and Material Removal Rate To test whether the discrepancies between the observed and expected frequencies can be attributed to chance, we use the statistic for test of goodness of fit for surface roughness and material removal rate as given by equation 9. (9) Criterion: Chosen for either to accept or reject the null hypothesis is: If χ2 > 8.672 (tabulated values), reject the null hypothesis Table 9 showed that χ2 = 0.0054 and 1.1078 for surface roughness and material removal rate respectively for 17 degrees of freedom where as degrees of freedom is given by: (rows-1) x (col-1) = (18-1) x (2-1) = 17 Therefore the analysis of data does suggest perception is correct with 95 % confidence level. Otherwise, there is reason to believe that the program does give correct output as shown in Table 9. 6. Confirmation Experiments The experimental study is carried out to validate the earlier developed empirical expressions for surface roughness and material removal rate. Depth of cut is least significant for surface roughness and cutting speed is least significant for material removal rate as observed for ANOVA Table 5 (a) and 6 (a). So depth of cut and cutting speed remained constant at 0.8 mm and 110.84 m/min respectively for validation and other parameter put the same level are shown in Table 2. To verify the goodness of the predicted model, the observed values and their predictive values of the surface roughness and material removal rate are given in the Table 10. Table 10 also shows the prediction error of output parameters i.e. surface roughness and material removal rate. It has been seen that the maximum and minimum error percentage for surface roughness is 8.235% and -7.509% and the maximum and minimum error percentage for material removal rate is 10.064% and -10.923%, which is very much satisfactory. Graphical comparison of actual and predicted values of surface roughness and material removal rate is shown in Figure 7 and Figure 8.

Surface Roughness Material Removal Rate

Expt. No. Prediction Value

Experimental Value % Error Prediction

Value Experimental

Value % Error

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

1.493 1.364 2.897 1.333 1.588 2.339 1.588 1.656 2.051 1.714 1.538 1.999 1.445 1.675 2.355 1.999 1.476 2.000

1.397 1.453 3.076 1.366 1.530 2.400 1.513 1.636 2.263 1.547 1.606 1.966 1.597 1.630 2.237 1.940 1.486 1.973

6.430 -6.525 -6.843 -2.476 3.652 -2.608 4.723 1.208

-10.336 9.743 -4.421 1.651

-10.519 2.686 5.011 2.951 -0.677 1.350

7.674 151.705 394.457 37.670

228.560 96.161

129.419 54.954

153.109 108.893 129.419 77.446 19.011

188.799 229.615 168.655 19.142

247.742

8.60 144.99 340.61 36.24

249.91 105.93 124.99 52.97

144.99 104.40 125.00 73.57 18.39

208.85 250.08 180.01 18.38

275.85

-12.067 4.426

13.651 3.796 -9.341

-10.159 3.422 3.610 5.303 4.126 3.414 5.003 3.266

-10.620 -8.913 -6.733 3.981

-11.346

∑=

−=

k

i i

ii

E)EO(

1

22χ


260

Table 9 Statistic for Test of Goodness of Fit Surface Roughness and Material Removal Rate *Test level of significance: α = 95%

Table 10 Validation between Experimental and Predicted Results (Surface Roughness and Material Removal Rate)

Surface Roughness Material Removal Rate Expt. No.

Observed Value

Expected Value (Oi – Ei) 2 / Ei

Observed Value

Expected Value (Oi – Ei) 2 / Ei

1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18

1.397 1.453 3.076 1.366 1.530 2.400 1.513 1.636 2.263 1.547 1.606 1.966 1.597 1.630 2.237 1.940 1.486 1.973

1.493 1.364 2.897 1.333 1.588 2.339 1.588 1.656 2.051 1.714 1.538 1.999 1.445 1.675 2.355 1.999 1.476 2.000

0.0061 0.0058 0.0110 0.0008 0.0021 0.0015 0.0035 0.0002 0.0219 0.0162 0.0030 0.0005 0.0159 0.0012 0.0059 0.0017 0.0001 0.0003

8.60 144.99 340.61 36.24

249.91 105.93 124.99 52.97

144.99 104.40 125.00 73.57 18.39

208.85 250.08 180.01 18.38

275.85

7.674 151.705 394.457 37.670

228.560 96.161

129.419 54.954

153.109 108.893 129.419 77.446 19.011

188.799 229.615 168.655 19.142

247.742

0.1117 0.2972 7.3506 0.0542 1.9943 0.9924 0.1515 0.0716 0.4305 0.1853 0.1508 0.1939 0.0202 2.1294 1.8239 0.7644 0.0303 3.189

Average χ2 = 0.0054 χ2 = 1.1078

Surface Roughness Material Removal Rate Expt. No. Prediction

Value Experimental

Value % Error Prediction Value

Experimental Value % Error

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

1.470 1.380 2.920 1.305 1.570 2.350 1.560 1.670 2.120 1.700 1.545 1.989 1.465 1.645 2.380 1.992 1.455 2.100

1.370 1.435 3.100 1.350 1.505 2.415 1.498 1.640 2.230 1.560 1.595 1.950 1.575 1.625 2.248 1.945 1.470 2.050

6.803 -3.985 -6.164 -3.448 4.140 -2.766 3.974 1.796 -5.189 8.235 -3.236 1.515 -7.509 1.216 5.546 2.359 -1.031 2.381

8.880 152.605 395.337 35.670

230.545 95.110

131.220 56.990

150.110 110.793 132.000 75.246 19.000

192.703 233.615 166.230 19.342

251.144

9.850 143.000 355.550 34.240

252.880 103.000 127.000 54.970

141.000 106.20

127.000 71.370 18.000

204.550 255.060 178.000 18.880

272.850

-10.923 6.294

10.064 4.009 -9.688 -8.296 3.216 3.544 6.069 4.146 3.788 5.151 5.263 -6.148 -9.180 -7.080 2.388 -8.643


261

Figure 7: Comparison between Actual and Predicted Values of Surface Roughness

Figure 8: Comparison between Actual and Predicted Values of Material Removal Rate

7. Utility Concept A customer evaluates a product on a number of diverse quality characteristics. To be able to make a rational choice, these evaluations on different characteristics should be combined to give a composite index. Such a composite index represents the utility of a product. The overall utility of a product measures the usefulness of that product in the eyes of the evaluator. The utility of a product on a particular characteristic measures the usefulness of that particular characteristic of the product. The overall utility of a product is the sum of utilities of each of the quality characteristics. Thus if xi is the measure of effectiveness of the attribute (characteristic) i and there are n attributes evaluating the outcome space, then the joint utility function can be expressed as (Bunn, 1982): U(x1, x2 , . . . , xn) = f[U1(x1), U2(x2), . . ., Un(xn)] (9) Where Ui (Xi) is the utility of the ith attribute The overall Utility function is the sum of individual utilities if the attributes are independent, and is given as follows:

U(X1, X2 , . . . , Xn) = ∑=

n

i ii Xu1

)( (10)

The attributes may be assigned weights depending upon the relative importance or priorities of the characteristics. The overall utility function after assigning weights to the attributes can be expressed as:

U(X1, X2 , . . . , Xn) = ∑=

n

i iii XuW1

)( (11) Where Wi is the weight assigned to the attribute i. The sum of the weights for all the attributes must be equal to 1. If the composite measure (the overall utility) is maximized, the quality characteristics considered for evaluation of utility will automatically be optimized (maximized or minimized what so ever the case may be).


262

8. Determination of Utility Value A preference scale for each quality characteristic is constructed. To determine the utility value for a number of quality characteristics later these scales are weighted to obtain a composite number (overall utility). The weighting is done to satisfy the test of indifference on the various quality characteristics. The preference scale should be a logarithmic one (Gupta and Murthy 1980). The minimum acceptable quality level for each quality characteristic is set out at 0 preference number and the best available quality is assigned a preference number of 9. If a log scale is chosen the preference number (Pi) is given by Eq. 12 (Gupta and Murthy, 1980).

⎟⎟⎠

⎞⎜⎜⎝

⎛= '

i

ii x

xAP log (12)

Where, Xi = value of any quality characteristic or attribute i X'

i = just acceptable value of quality characteristic or attribute i A = constant The value of A can be found by the condition that if Xi = X* (where X* is the optimal or best value), then Pi = 9 Therefore,

⎟⎟⎠

⎞⎜⎜⎝

⎛=

'iX

XA

*

log

9 (13)

Subject to the condition:

∑==

n

i iW1

1 (14)

The overall utility can be calculated as follows:

∑==

n

i ii PWU0

(15) Among various quality characteristics type viz. smaller the better, higher the better, and nominal the better suggested by Taguchi, the Utility function would be higher the better type. Therefore, if the Utility function is maximized, the quality characteristics considered for its evaluation will automatically be optimized (maximized or minimized as the case may be). The stepwise procedure for carrying out multi-response optimization with Utility concept and Taguchi method is illustrated as 1. Use the Taguchi matrix experimental design and analysis to find out the optimal value of each of the selected process

responses. 2. Construct a preference scale for each response based on their optimal value and minimum acceptable level (Eqs.12 & 13). 3. Assign weights (Wi) based on the experience and customer preference, keeping in view that the total sum of weights is equal

to 1 such that the (Eq. 14). 4. Find overall utility values for different experimental trial conditions considering all the responses involved in multi-response

optimization (Eq. 15). 5. Use the values determined in step 4 as raw responses of different trial conditions of the experimental matrix. If trials are

repeated, find S/N ratios (HB type), as the utility is a higher-the-better type characteristic (Roy, 1990). 6. Analyze the results as per the standard procedure suggested by Taguchi (Roy, 1990). 7. Find the optimal settings of process parameters for mean and S/N utility based on the analysis performed in step 6. 8. Predict optimal values of different response characteristics for the optimal parametric setting that maximizes the overall

utility as determined in step 7. 9. Conduct confirmation experiments to verify the optimal results. Based upon the methodology developed in the previous sections, following case have been considered to obtain the optimal settings of the process parameters of lathe turning for predicting the optimal values of combined responses. The two quality characteristics (Surface Roughness (Ra) and Material Removal Rate (MRR)) are included in utility response. Taguchi L18 orthogonal array (OA) (Roy, 1990) has been adopted for conducting the experiments. Tool nose radius (A), tool rake angle (B), feed rate (C), cutting speed (D), cutting environment (E) and depth of cut (F) are selected as input parameters. Response parameters (quality characteristics) are Surface Roughness (Ra) and Material Removal Rate (MRR) when they are optimized individually; the summary of results is produced in Table 11.


263

Table 11 Optimal Setting and Values of Process Parameters (Individual Quality Characteristics optimization)

* C – feed rate, D – cutting speed and F – depth of cut ** Subscripts represent levels of the process parameters. The optimal settings of process parameters and the optimal values of Surface roughness and material removal rate (when they are optimized individually) have already been established by using Taguchi’s design of experiment. Following is the stepwise procedure for transforming experimental data into utility data. (i) Construction of preference scales

(a) Surface Roughness (Ra) X* = optimum value of Ra (when optimized individually) = 1.311μm (Table 11) X/

i = maximum acceptable value of Ra = 3.0 μm (Table 4) assumed (All the Ra values in Table 4 are in between: 1.23 and 3.44 μm) Using these values and the Eq. 11 & Eq. 12, the following preference scale for Ra has been found:

⎟⎠⎞

⎜⎝⎛−=

03log0725

.x.P i

Ra (16)

(b) Material Removal Rate (MRR) X* = optimum value of material removal rate (when optimized individually) = 301.98 mm3/ sec. (Table 11) X/

i = minimum acceptable value of material removal rate = 8 mm3/ sec. (Table 4) assumed (All the material removal rate values in Table 4 are in between: 8.50 and 347.23 mm3/sec.) Using these values and the Eq. 11 & Eq. 12, the following preference scale for material removal rate has been found:

⎟⎠⎞

⎜⎝⎛=

08log7115

.x.P i

MRR (17)

(ii) Weights of quality characteristic

It has been assumed that both the quality characteristics are equally important and hence an equal weight has been assigned. However, there is no constraint on the weights and it can be any value between 0 and 1 subjected to the condition specified in Equation 14 (Singh and Kumar, 2006). WRa = weights for Ra = 1/2 WMRR = weights for MRR = 1/2

(iii) Utility value calculation

The following relation was used to calculate the utility function based upon the experimental trials:

U (n, R) = PRa (n, R) x WRa + PMRR (n, R) x WMRR (18)

Where, n is the trial number (n = 1, 2, 3… 18) and R is the repetition number (R = 1, 2, 3). The calculated Utility values are shown in Table 12.

Quality Characteristics

Optimal Level of Process Parameters

Significant Process Parameters (at 95% confidence level)

Predicted Optimal Value of Quality Characteristics

Surface Roughness Material Removal Rate

C2D2F2 C3D3F3

C, D, F C, D, F

1.311 μm 301.98 mm3/sec.


264

Table 12 Calculated Utility Data Based on Responses (a) Surface Roughness (b) Material Removal Rate

9. Determination of Optimal Settings of Process Parameters The data (utility values) have been analyzed both for mean response (mean of utility at each level of each parameter) and signal-to-noise (S/N) ratio. Since utility is a higher-the-better (HB) type of quality characteristic, (S/N) HB has been used. The average and main response in terms of Utility values and S/N ratio (Tables 15 and 16) are plotted in Figure 9 (a-f). It can be observed from Figure 9 (a-f) that the 2nd level of tool nose radius (A2), 2nd level of tool rake angle (B2), 2nd level of feed rate (C2), 2nd level of cutting speed (D2), 2nd level of cutting environment (E2) and 2nd level of depth of cut (F2) are expected to yield a maximum values of the utility and S/N ratio within the experimental space. The pooled version of ANOVA for utility data and S/N ratio are given in Tables 13 and 14 respectively. It can be noticed from Table 13 that the input parameters feed rate (C), cutting speed (D), cutting environment (E) and depth of cut (F) significant effect (at 95% confidence level) on the utility function. On the other hand, from Table 14 shows that the feed rate and depth of cut have significant effect on the S/N ratio of utility function. So, other insignificant parameters for S/N ratio can be taken as economy factor. The optimal values of utility and thus the optimal values of response characteristics in consideration are predicted at the above levels of significant parameters.

Table 13 Pooled ANOVA (Raw Data: Surface Roughness and MRR)

SS = sum of squares, DOF = degrees of freedom, variance (V) = (SS/DOF), T = total, SS/ = pure sum of squares, P = percent contribution, e = error, Fratio = (V/error), Tabulated F-ratio at 95% confidence level F0.05; 1; 42 = 4.08, F0.05; 2; 42 = 3.23, * Significant at 95% confidence level

Trial No. Raw Data (Utility Values) S/N Ratio (db) R1 R2 R3

1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18

4.312 6.776 4.603 6.373 7.364 5.271 6.790 5.528 4.732 7.410 7.104 4.341 4.553 8.192 6.098 5.753 5.882 6.647

3.997 7.889 5.062 5.746 8.082 3.326 7.831 5.152 5.284 5.884 7.442 5.234 4.553 6.640 7.038 6.630 4.691 7.61

4.452 8.016 3.934 6.335 7.512 4.843 6.828 6.302 5.384 7.220 5.976 5.645 4.277 7.355 5.692 6.342 4.127 5.880

12.5485 17.4950 12.9861 15.7497 17.9331 12.4917 17.0300 14.9676 14.1653 16.5574 16.5842 13.9451 12.9772 17.2841 15.1096 15.8599 13.5308 16.3938

Source SS DOF V F ratio Prob. SS/ P (%)

Tool nose radius(A) Tool rake angle(B) Feed rate(C) Cutting speed(D) Cutting Environment(E) Depth of cut(F) T

e (pooled)

0.7805 0.4346 15.5603 6.6768 3.8117 36.4492

1 2 2 2 2 2

0.7805 0.2173 7.7802 3.3384 1.9058 18.2246

0.5069

Pooled Pooled 15.35* 6.59* 3.76*

35.95*

0.222 0.654 0.000 0.003 0.031 0.000

--- ---

14.546 5.663 2.797 35.435

--- ---

17.11 6.66 3.29 41.67

85.0045 21.2914

53 42

85.0045 26.867

100.00 31.60


265

Table 14 S/N Pooled ANOVA (Raw Data: Surface Roughness and MRR)

Tabulated F-ratio at 95% confidence level F0.05; 1; 6 = 5.99, F0.05; 2; 6 = 5.14

Table 15 Main Effects of Utility (Raw Data: Surface Roughness and MRR)

= Table 16 Average S/N Ratio values and main effects (Surface Roughness and MRR)

(a)

(b)

(c) (d)

Figure 9: Utility value and S/N ratio (a) effect of tool nose radius, (b) effect of tool rake angle, (c) effect of feed rate, (d) effect of cutting speed

Source SS DOF V F ratio Prob. SS/ P (%)

Tool nose radius(A) Tool rake angle(B) Feed rate(C) Cutting speed(D) Cutting Environment(E) Depth of cut(F)

T e (pooled)

0.8434 0.3861 11.4733 4.5265 3.2354 29.9230

1 2 2 2 2 2

0.8434 0.1930 5.7367 2.2632 1.6177 14.9615 0.7717

Pooled Pooled

7.43* Pooled Pooled

19.39*

0.336 0.786 0.024 0.129 0.204 0.002

--- ---

9.929 --- ---

28.379

--- ---

18.05 --- ---

51.58 55.0179 4.6303

17 6

55.0179 13.119

100.00 23.84

Nose radius (A)

Tool rake angle (B)

Feed rate (C)

Cutting speed (D)

Cutting Environment (E)

Depth of cut (F)

Level 1 Level 2 Level 3

Differences(Δ�)

5.842 6.082

--- 0.240

5.850 6.069 5.966 0.220

5.849 6.668 5.368 1.300

5.592 6.435 5.858 0.842

6.139 6.161 5.586 0.574

4.805 6.632 6.449 1.827

Nose radius (A)

Tool rake angle (B)

Feed rate (C)

Cutting speed (D)

Cutting Environment (E)

Depth of cut (F)

Level 1 Level 2 Level 3

Differences(Δ)�

15.01 15.44

--- 0.43

15.02 15.34 15.32 0.32

15.12 16.25 14.31 1.95

14.74 15.92 15.02 1.18

15.39 15.65 14.65 1.00

13.41 16.27 15.99 2.86


266

(e) (f)

Figure 9: Utility value and S/N ratio (e) effect of cutting environment, (f) effect of depth of cut.

Table 17 Average values of various responses at optimal levels

*The average values are taken from experimental data. 10. Optimal Values of Quality Characteristics (Predicted Means Surface Roughness) The average values of all the response characteristics at the optimum levels of significant parameters with respect to Utility function are recorded in Table 17. *The average values are taken from experimental data. The optimal values of the predicted means (μ) of different response characteristics can be obtained from the following equation: µRa = TRa + ﴾ C2− TRa) + ﴾ D2− TRa) + ﴾E2− TRa) + ﴾F2− TRa) C2 = second level of feed rate, D2 = second level of cutting speed, E2 = second level of Cutting environment cut, F2 = second level of depth of cut, TRa = Overall mean Where TRa = overall mean of surface roughness = 1.812 (Table 4)

C2, D2, E2 and F2 are the mean values of surface roughness with parameters at optimum levels. C2 =1.557, D2 =1.672, E2 =1.767, F2 =1.706 (Table 17): Hence µRa = 1.266 A confidence interval for the predicted mean on a confirmation run can be calculated using the equation 19 and 20 respectively (Ross, 1996):

eff

eeaPOP n

VfFCI ) (1,= (19)

⎥⎥⎦

⎤

⎢⎢⎣

⎡+=

RnVfFCI

effeeaCE

11) (1, (20)

Where Fα; (1, fe) = F0.05; (1; 42) = 4.08 (tabulated). α = risk = 0·05, fe = error DOF = 42 Table 5 (A) N = total number of experiments = 18 Ve = error variance = 0.07039 Table 5 (A) Total DOF associated with the mean (µRa) = 11, Total trial =18, N=18×3 = 54, neff = effective number of replications

Levels Surface Roughness (µm) Material Removal Rate (mm3/sec.) C2 D2 E2 F2

1.557 1.672 1.767 1.706

133.35 147.95 122.98 152.55


267

mean] theof estimate with theassociated DOF [Total1+=

Nneff

neff = 54 / (1 + 11) = 4.5 R = number of repetitions for confirmation experiment = 3 CIPOP = 0.253 CICE = 0.399

The 95% confidence interval of the population is: [µRa − CI] < µRa < [µRa + CI] i.e. 1.013 < µRa < 1.519 The 95% confidence interval of the predicted optimal surface roughness is: [µRa − CI] < µRa < [µRa + CI] i.e. 0.867 < µRa < 1.665 MRR: µMRR = TMRR + ﴾ C2− TMRR) + ﴾ D2− TMRR) + ﴾E2− TMRR) + ﴾F2− TMRR) Where TMRR = overall mean of material removal rate = 136.875 (Table 4) C2, D2, E2 and F2 are the mean values of material removal rate with parameters at optimum levels. C2 =133.35, D2 =147.95, E2 =122.98, F2 =152.55 (Table 17): Hence µMRR = 146.205 The following values have been obtained by the ANOVA:

N = 54, fe = 42, Ve = 1189 Table 6 (A), neff = 4.5, R = 3, F0.05 (1, 42) = 4.08

A confidence interval for the predicted mean on a confirmation run can be calculated using the equation 19 and 20 respectively.

CIPOP = 32.833 CICE = 51.889

The 95% confidence interval of the population is: [µMRR − CI] < µMRR < [µMRR + CI] i.e. 113.372 < µMRR < 179.038

The 95% confidence interval of the predicted optimal material removal rate is: [µMRR − CI] < µMRR < [µMRR + CI] i.e. 94.316 < µMRR < 198.094

The optimal values of process variables at their selected levels are as follows: Parameter Level Feed Rate (C) 2 (0.1 mm/ rev) Cutting Speed (D) 2 (110.84 m/ min) Cutting Environment (E) 2 (Wet) Depth of Cut (F) 2 (0.8 mm)

11. Confirmation Experiments Three experiments are performed at optimal settings as suggested by Taguchi analysis of Utility data. The average value of surface roughness and material removal rate, while turning UD-GFRP with PCD tool is found to be 1.411µm and 195.033mm3/sec. This result is within the 95% confidence interval of the predicted optimal value of the selected machining characteristic (surface roughness and material removal rate). Hence the optimal settings of the process parameters, as predicted in the analysis, can be implemented. Shows the conformance of results obtained in ANOVA as well as the results obtained using confirmation. 12. Genetic Algorithm (GA) Genetic algorithms are search methods that employ processes found in natural biological evolution. These algorithms search or operate on a given population of potential solutions to find the optimum solution. To do this, the algorithm applies the principle of survival of the fittest to find better and better approximations. At each generation, a new set of approximations is created by the process of selecting individual potential solutions (individuals) according to their level of fitness in the problem domain and breeding them together using operators borrowed from natural genetics. This process leads to the evolution of populations of individuals that are better suited to their environment than the individuals that they were created from, just as in natural adaptation. The GA generally includes the three fundamental genetic operations of selection, crossover and mutation. These operations are used to modify the chosen solutions and select the most appropriate offspring to pass on to succeeding generations. GAs consider many points in the search space simultaneously and have been found to provide a rapid convergence to a near optimum solution in many types of problems; in other words, they usually exhibit a reduced chance of converging to local minima. GA suffers from the problem of excessive complexity if used on problems that are too large.


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The GA works with a population of feasible solutions and, therefore, it can be used in multi-objective optimization problems to simultaneously capture a number of solutions (Kuriakose and Shunmugam, 2005). The non-dominate sorting Genetic Algorithm (NSGA-II) which was introduced by (Mandal, 2007). It is a powerful general purpose optimization tool to solve optimizing problems in mathematics and engineering. This algorithm is fast, but it has been as a controversial method and has been opposed due to some difficulty and complexity when it comes to computational approach. The Non-dominating Sorting GA-II (NSGA-II) is a fast, elitist multi-objective genetic algorithm that is widely used for generating the Pareto frontier. Its main advantage in solving multi-objective problems is that it leads the search toward the global Pareto front while maintaining diversity of the solution set along that front (Akundi et al., 2005). So, both single and multi-objective optimization genetic algorithms can be used in the given parametric combination. 13. Conclusions

• From the experimental results, it is evident that the surface roughness increases as feed rate increases. • From S/N ratio and response table, it is observed that the feed is the most influencing parameter for surface roughness. By

increasing the feed, the surfaces roughness increases. The higher feed rate led cutting tool to traverse the work piece so rapidly that deteriorates the surface quality.

• For achieving good surface finish on the unidirectional glass fiber reinforced plastic composite using polycrystalline diamond insert, larger tool nose radius, moderate tool rake angle, moderate feed rate, moderate cutting speed, environment (dry) and moderate depth of cut were preferred. The optimal parametric combination for polycrystalline diamond insert cutting insert was reported as A2, B2, C2-D2-E1 and F2.

• Feed rate is the factor, which has great influence on surface roughness, followed by cutting speed. • From the ANOVA result, it is concluded that C – feed rate, D – cutting speed, F – Depth of cut, have significant effect on

material removal rate A, B, E have no effect at 95% confidence level. It is found that depth of cut is more significant factor than other parameters, whilst cutting speed is the least significant parameter.

• The second-order model for surface roughness and material removal rate has been developed from the observed data. The prediction error of output parameters i.e. surface roughness and material removal rate. It was found that the maximum and minimum error percentage for surface roughness is 8.235% and -7.509% and the maximum and minimum error percentage for material removal rate is 10.064% and -10.923%, which is very much satisfactory.

• The multiple performance characteristics are surface roughness and material removal rate. On the basis of Taguchi approach and Utility concept, a model was developed to achieve this. Based on the ANOVA significant process parameters for multiple performances are depth of cut, feed rate, cutting speed and cutting environment has significant effect on the utility function. The percentage contribution of Depth of cut (41.67%), Feed rate (17.11%), Cutting speed (6.66%) and cutting environment (3.29%). It is found that the proposed model based on Taguchi approach and Utility concept is simple, useful and provides an appropriate solution for multi-response optimization problems.

• The 95% confidence interval of the predicted optimal surface roughness is: [µRa − CI] < µRa < [µRa + CI] i.e. 0.867 < µRa < 1.665

• The 95% confidence interval of the predicted optimal material removal rate is: [µMRR − CI] < µMRR < [µMRR + CI] i.e. 94.316 < µMRR < 198.094

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Estimates of parameters Exponentially determined constant logarithmic transformations of machining parameters Surface Roughness Material Removal Rate


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A B C D E F K η y ε Ŷ χ2

Tool nose Radius / mm Tool Rake angle / Degree Feed rate / (mm/rev) Cutting speed / (m/min.) & rpm Cutting environment Depth of cut / mm Constant Surface Roughness & MRR response Measured Surface Roughness & MRR Experimental error Estimated response based on second order model (µm & mm3/sec.) Chi-square

Biographical notes Mr. Surinder Kumar is a Research Scholar in the Department of Mechanical Engineering, National Institute of Technology, Kurukshetra-136119,( Haryana), India. He was graduated in Mechanical Engineering from S.K.I.E.T, Kurukshetra, Haryana and Post graduated in the specialization of Manufacturing System from M.M Engineering College Mullana, Ambala (Haryana). At present he is pursuing (FULL-TIME) Ph.D from NIT Kurukshetra, Haryana, India. He has more than 2 years of experience in teaching. His current area of research includes Machining of composite materials, Optimization, Modeling. Dr. (Mrs.) Meenu Gupta is an Associate Professor in the Department of Mechanical Engineering, National Institute of Technology, Kurukshetra-136119, (Haryana), India. She has more than 25 years of experience in teaching and research. Her current area of research includes Machine vision, Image processing, Optimization, Modeling. Dr. P.S. Satsangi is an Associate Professor in the Department of Mechanical Engineering, PEC University of Technology Chandigarh, India. He has more than 25 years of experience in teaching and research. His current area of research includes Machining of composite materials, Modern manufacturing, Optimization, Modeling. Dr. H.K. Sardana is a Scientist ‘G’ & Head, in the Department of Computational Instrumentation, CSIO, Chandigarh-160030, India. His current area of research includes, Signal Processing, Computer Aided Design and Simulation, Human Physiology and Bio-Instrumentation, Digital Image Processing, Soft Computing Techniques, Computer Aided Metrology and Machine Vision. Received December 2011 Accepted May 2012 Final acceptance in revised form June 2012

modeling and analysis for surface roughness and material

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